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Homework Help: Reynolds number and the relationship with lift and drag.

  1. Oct 22, 2012 #1

    I am preparing for my aerodynamics exam and I'm having trouble with this question.

    Why is the Reynolds number of the airflow over a wing important in determining the value of lift and drag

    The Reynolds number is important for determining laminar and turbulent flows over a body. It is a dimensionless number and expresses
    the ratio of inertial forces to viscous forces. A Reynolds number less than 5 x 105 is likely to be laminar whereas a Reynolds number greater
    than 5 x 105 will most likely be turbulent.

    The Reynolds number is important for determining drag as we can use it to calculate the length of the laminar and turbulent flow
    over a wing. Moreover we can use this to calculate the friction coefficient (skin friction drag) acting on the wing.

    Laminar Flow

    Cf = [itex]\frac{1.328}{\sqrt[]{}Re}[/itex]

    Turbulent Flow

    Cf = [itex]\frac{0.074}{\sqrt[]{}Re^{2}}[/itex]

    It is important for calculating lift because as Reynolds number increases, the maximum lift coefficient increases. But this does not occur
    indefinitely; when flows become very turbulent, the maximum lift coefficient begins to drop and so does the overall lift coefficient.

    Re = [itex]\frac{ρV×}{\mu}[/itex]

    ρ = Density
    V = Velocity of the free-stream airflow
    × = The characterised length of the aerofoil
    [itex]\mu[/itex] = The fluid viscosity

    I would like to know if the way I have explained the Reynolds number is correct particularly with reference to lift, and is the Reynolds number important when
    dealing with other types of drag?

  2. jcsd
  3. Oct 22, 2012 #2


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    Gold Member

    This is not true. 5 x 105 is actually an extraordinarily low Reynolds number (based on chord length or downstream distance) and will almost never be turbulent for the average situation. There is no general transition Reynolds number that you can quote in the way that you have.

    The most important effect that Reynolds number has on lift is in its effect on the boundary layer thickness and thus the displacement thickness. That affects the effective thickness of the airfoil and thus the lift. Turbulent flows also have a profound effect on separation, which have their own profound effect on lift. How exactly those two things affect lift is up to you to discover for the moment. It's your homework after all. ;-)
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